Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26012289 | C2 | semidirect |
| 2. #26012058 | C2 | semidirect |
| 3. #26011669 | C2 | semidirect |
| 4. #26011659 | C2 | semidirect |
| 5. #26011508 | C2 | semidirect |
| 6. C2×#19149596 | C2 | semidirect |
| 7. C2×H(5,𝔽2)×C173 | C2 | semidirect |
| 8. C2×#14583826 | C22 | semidirect |
| 10. #19149709 | C22 | semidirect |
| 12. #19149704 | C22 | semidirect |
| 14. C2×#14583810 | C22 | semidirect |
| 15. #19149675 | C22 | semidirect |
| 16. #19149666 | C22 | semidirect |
| 19. #19149638 | C22 | semidirect |
| 20. #19149606 | C22 | semidirect |
| 21. #19149596 | C22 | semidirect |
| 32. C2×Dic346 | C23 | semidirect |
| 33. C2×D692 | C23 | semidirect |
| 42. #14583810 | C23 | semidirect |
| 47. C4×Dic173 | C23 | semidirect |
| 54. #41×C173 | D4 | semidirect |
| 56. C2×Q8×C173 | D4 | semidirect |
| 66. C2×D4×C173 | D4 | semidirect |
| 131. C173 | #3019 | semidirect |
| 133. C2×H(5,𝔽2) | D173 | semidirect |
| 170. #41 | C22⋊D173 | semidirect |
| 173. C2×Q8 | C22⋊D173 | semidirect |
| 186. C2×D4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #26012058 | 2 |
| #26011669 | 2 |
| #26011659 | 2 |
| #26011508 | 2 |
| C2×#19149596 | 2 |
| C2×H(5,𝔽2)×C173 | 2 |
| #3019 | 173 |